粘滞宇宙学相关问题研究

【作者】 杨静；

【导师】 翟向华；

【作者基本信息】 上海师范大学 ， 数学物理， 2024， 博士

【摘要】 观测表明宇宙当前处于加速膨胀阶段,解释这种加速的一个最直接方式是将宇宙学常数找回扮演暗能量的角色。尽管这一模型已经被证明是相当准确和成功的,但从理论角度来看宇宙学常数缺乏物理起源,其观测值过小无法用任何基本理论来解释。为了缓解或者解决这些问题,一些试探性的解决方案是试图引进新的未知的物质,比如最简单的引入标量场。理论上总能唯象地构造一个合适的势能,使得引入的标量场的演化能符合观测。另一个解决这些问题的角度是考虑修正引力,将广义相对论视为待发现的真实引力理论的近似。然而无论是在广义相对论还是修正引力的框架下,宇宙介质通常被简化为理想流体。从流体动力学的角度来看,非理想流体可能由于耗散效应从而偏离热平衡,这种在宇宙膨胀中包括热传导、体粘滞和剪切粘滞的耗散过程已经被仔细研究。本文着重研究了两类粘滞宇宙学模型。首先,在f(T)引力框架下,我们提出了一种新的粘滞模型,可以适用于宇宙的不同时期。考虑到现实宇宙中物质流体的粘滞性可能源于热力学效应,我们提出的新模型将体粘滞作为对重子和暗物质的理想流体模型的修正。其次,我们还研究了一个包含体粘滞的phantom暗能量模型,探索了其作为解决phantom暗能量模型中大撕裂奇点问题的潜在方法。为验证模型的有效性,本文使用最新的观测数据来约束两类暗能量模型,对模型参数进行拟合。并利用拟合结果通过一些宇宙学分析方法进一步探究了当考虑粘滞效应后宇宙的演化行为。我们发现体粘滞作为一种物理修正,不仅能够提高宇宙学模型的适用性,还在宇宙演化行为和缓解宇宙奇异性问题方面扮演着关键角色,这些发现为粘滞宇宙学模型在宇宙学研究中的应用提供了有力支持,同时也推动我们进一步深入的理解暗能量性质。第二章主要介绍了宇宙学理论基础与粘滞宇宙学理论基础。第三章介绍了两类粘滞暗能量模型基本情况。第四章中对Ia型超新星、宇宙微波背景辐射、重子声学振荡等观测数据和分析方法进行介绍,并利用观测数据对两类粘滞模型参数进行拟合。第五章中,利用观测数据对模型参数的拟合结果,分别对两类粘滞暗能量模型应用诊断分析,探究粘滞性在整个宇宙演化中的作用。在第六章中,进一步研究具有体粘滞的phantom暗能量模型的宇宙学含义,探索这一模型作为一种解决大撕裂奇点问题的可能方法。利用最新观测数据来约束模型参数,对模型进行了动力学分析,探讨了体粘滞在宇宙晚期行为和缓解phantom宇宙的奇异性问题方面的作用。更多还原

【Abstract】 Observations suggest that the universe is currently in an accelerated expansion phase,and one of the most straightforward ways to explain this acceleration is to retrieve the cosmological constant to play the role of dark energy.Although this model has proved to be quite accurate and successful,from a theoretical point of view the cosmological constant lacks a physical origin and its observed value is too small to be explained by any fundamental theory.In order to alleviate or solve these problems,some tentative solutions have attempted to introduce new unknowns,such as the simplest introduction of a scalar field model.It is always theoretically possible to construct a suitable potential exclusively,so that the evolution of the introduced scalar field can be consistent with the observations.Another perspective to address these issues is to consider modified gravity,treating general relativity as an approximation of the true theory of gravity to be discovered.However,in the framework of both general relativity and modified gravity,the cosmic medium was usually reduced to an ideal fluid.From a hydrodynamic point of view,non-ideal fluids may deviate from thermal equilibrium due to dissipative effects.Such dissipative processes,which include heat conduction,bulk viscosity and shear viscosity,may affect the expansion of the universe.Some related topics have been carefully studied.Two types of viscous cosmological models are investigated in this paper.Firstly,in the framework of f(T)gravity,we propose a new viscous model that can be applied to different periods of the universe.Considering that the viscosity of matter fluids in the real universe may originate from thermodynamic effects,the new model uses bulk viscosity as a modification to the ideal fluid model for baryons and dark matter.Secondly,we also study a phantom dark energy model with including bulk viscosity and explore it as a potential solution to the problem of big rip singularities in phantom dark energy models.To examine the validity of the models,in this paper,we use the latest observational data to constrain the two types of dark energy models and fit the model parameters.The fitting results are also used to further explore the evolutionary behaviour of the universe when viscous effects are taken into account through a number of cosmological analyses.We find that bulk viscosity,as a physical correction,not only improves the applicability of cosmological models,but also plays a key role in the evolutionary behaviour of the universe and alleviates the problem of cosmic singularity.These findings provide a strong support for the application of viscous cosmological models in cosmological studies,and at the same time push us to further deepen our understanding of the nature of dark energy.In Chapter 2,we focuse on the theoretical foundations of cosmology and viscous cosmology.In Chapter 3,the basics of the two types of viscous dark energy models are presented.In Chapter 4,the observational data and analysis methods of type Ia supernovae,cosmic microwave background radiation,and baryon acoustic oscillations are introduced,and the parameters of the two types of viscous models are fitted using the observational data.In Chapter 5,the results of fitting the model parameters with observational data are used to apply diagnostic analyses to the two types of viscous dark energy models.In Chapter6,we further investigate the cosmological implications of phantom dark energy models with bulk viscosity,exploring this model as a possible solution to the problem of big rip singularities.Using the latest observational data to constrain the model parameters,a dynamical analysis of the model is carried out to explore the role of bulk viscosity in the late-time behaviour of the universe and in alleviating the singularity problem of the phantom universe.更多还原